What I'm trying to get through my head here is how taking the Laplace transform of a system with a position function like
$X(t)=t$
is possible.
To my current (admittedly incomplete) understanding, what a Laplace transform is doing to a system physically is defining it in terms of its frequency based on its time function. However, the frequency of a system is defined as the number of cycles it goes through in a given amount of time, and if its position function looks like the above one (or any non-periodic function of $t$) I don't see how it's possible to define it in terms of frequency, and yet the transform of such a system is given as:
$L[X(t)]=\frac{1}{s^2}$
If anyone could explain this it'd be greatly appreciated.